On Fermat's principle for causal curves in time oriented Finsler spacetimes
Differential Geometry
2015-06-04 v2 General Relativity and Quantum Cosmology
Abstract
In this work, a version of Fermat's principle for causal curves with the same energy in time orientable Finsler spacetimes is proved. We calculate the secondvariation of the {\it time arrival functional} along a geodesic in terms of the index form associated with the Finsler spacetime Lagrangian. Then the character of the critical points of the time arrival functional is investigated and a Morse index theorem in the context of Finsler spacetime is presented.
Keywords
Cite
@article{arxiv.1202.3869,
title = {On Fermat's principle for causal curves in time oriented Finsler spacetimes},
author = {Ricardo Gallego Torromé and Paolo Piccione and Henrique Vitório},
journal= {arXiv preprint arXiv:1202.3869},
year = {2015}
}
Comments
20 pages, minor corrections, references added